Schrödinger's Cat and Gravity

I realize that Schrodinger intended this thought experiment as a way to show how absurd the interpretation of a cat being in two states was. I don't understand how that interpretation can be entertained in the first place due to gravity.

Say you were measuring the gravitational field (very accurately) around the experiment. You could detect whether the cat was alive or dead based on its effect on gravity (either cause it's moving around or not or breathing or not). Thus the cat's state is "measurable" without interacting it through the wave function.

Similarly for any "multiple worlds" interpretation of qm--if there are multiple worlds why can't we measure the alternative wave functions through their gravitation effects on the "version" of the wave functions we live in?

Say you were measuring the gravitational field (very accurately) around the experiment. You could detect whether the cat was alive or dead based on its effect on gravity (either cause it's moving around or not or breathing or not). Thus the cat's state is "measurable" without interacting it through the wave function.

Its gravitational field IS an interaction. No different if the cat were charged, and you monitored its Coulomb field.